In a magnetic tape cassette described in the German Auslegeschrift 2 131 731, two cassette reels float within the interior of the cassette housing and are aligned both axially and radially within the cassette only after insertion within the magnetic tape recorder. In this design, the inside diameter of the tape reel hubs is different, which is an advantage from the point of view of the uniformity of the components within the system. Furthermore, the known cassette makes no provision for removing the reels individually so as to be used on a magnetic tape recorder of the reel-to-reel type. Further known in the art is a tape cassette with a single reel and an endless tape loop in which the tape passes an open end of the cassette over pivotable arms.